Problem: Simplify the following expression: $ n = \dfrac{-9y - 9}{3y} + \dfrac{1}{8} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-9y - 9}{3y} \times \dfrac{8}{8} = \dfrac{-72y - 72}{24y} $ Multiply the second expression by $\dfrac{3y}{3y}$ $ \dfrac{1}{8} \times \dfrac{3y}{3y} = \dfrac{3y}{24y} $ Therefore $ n = \dfrac{-72y - 72}{24y} + \dfrac{3y}{24y} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-72y - 72 + 3y}{24y} $ $n = \dfrac{-69y - 72}{24y}$ Simplify the expression by dividing the numerator and denominator by 3: $n = \dfrac{-23y - 24}{8y}$